Abstract

[Parts I and II of this article were published in Optimization 53 (2004) 165–177 and 529–547.] This paper studies the class of increasing and co-radiant (ICR) functions over a cone equipped with an order relation which agrees with the conic structure. In particular, a representation of ICR functions as abstract convex functions is provided. This representation suggests the introduction of some polarity notions between sets. The relationship between ICR functions and increasing positively homogeneous functions is also shown.

Author information

Contact details are reproduced from the original publication and may be historical.

Joydeep Dutta

Dept. of Mathematics and Statistics, Indian Institute of Technology, Kanpur, 208016 Kanpur, India

jdutta@iitk.ac.in

Juan Enrique Martínez-Legaz

Dep. d'Economia i d'Història Economica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

JuanEnrique.Martinez@uab.es

Alex M. Rubinov

CIAO – SITMS, University of Ballarat, P.O. Box 663, Ballarat, Vic. 3353, Australia

Keywords

  • Monotonic analysis
  • ICR functions
  • abstract convexity
  • radiant sets
  • co-radiant sets
  • normal sets
  • co-normal sets

Mathematics Subject Classification

26B25, 26A48

Suggested citation

J. Dutta, J. E. Martínez-Legaz, A. M. Rubinov. “Monotonic Analysis over Cones: III.” Journal of Convex Analysis 15 (2008), No. 3, 561–579.

Copyright Banach Press 2008